Pattern-Based Graph Abstraction

We present a new abstraction technique for the exploration of graph transformation systems with infinite state spaces. This technique is based on patterns, simple graphs describing structures of interest that should be preserved by the abstraction. Patterns are collected into pattern graphs, layered graphs that capture the hierarchical composition of smaller patterns into larger ones. Pattern graphs are then abstracted to a finite universe of pattern shapes by collapsing equivalent patterns. This paper shows how the application of production rules can be lifted to pattern shapes, resulting in an over-approximation of the original system behaviour and thus enabling verification on the abstract level.